The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure
Oksana E. Hentosh , Yarema A. Prykarpatskyy , Aleksandr Balinsky , Anatolij K. Prykarpatsky
AbstractThere are reviewed modern investigations devoted to studying nonlinear dispersiveless heavenly type integrable evolutions systems on functional spaces within the modern differential-geometric and algebraic tools. Main accent is done on the loop diffeomorphism group vector fi elds on the complexifi ed torus and the related Lie-algebraic structures, generating dispersionless heavenly type integrable systems. As examples, we analyzed the Einstein–Weyl metric equation, the modifi ed Einstein–Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations, the inverse fi rst Shabat reduction heavenly equation, the fi rst and modifi ed Plebański heavenly equations,the Husain heavenly equation, the general Monge equation and the classical Korteweg-de Vries dispersive dynamical system. We also investigated geometric structures of a class of spatially one-dimensional completely integrable Chaplygin type hydrodynamic systems, which proved to be deeply connected with differential systems on the complexifi ed torus and the related diffeomorphism group orbits on them.
|Journal series||Annals of Mathematics and Physics, ISSN 2689-7636, e-ISSN 2689-7636, (0 pkt)|
|Publication size in sheets||0.7|
|Keywords in English||Lax–Sato equations; Multi-diemnsional integrable heavenly equations; Lax integrability; Hamiltonian system; Torus diffeomorphisms; Loop lie algebra; Lie-algebraic scheme; Casimir invariants; R-structure; Lie-poisson structure; Conformal structures; Superalgebras; Super-integrable systems|
|License||Journal (articles only); author's original; ; after publication|
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